{"paper":{"title":"On syndetic Riesz sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Itay Londner, Marcin Bownik","submitted_at":"2018-07-07T06:29:55Z","abstract_excerpt":"Applying the solution to the Kadison-Singer problem, we show that every subset $\\mathcal{S}$ of the torus of positive Lebesgue measure admits a Riesz sequence of exponentials $\\left\\{ e^{i\\lambda x}\\right\\} _{\\lambda \\in \\Lambda}$ such that $\\Lambda\\subset\\mathbb{Z}$ is a set with gaps between consecutive elements bounded by ${\\displaystyle \\frac{C}{\\left|\\mathcal{S}\\right|}}$. In the case when $\\mathcal{S}$ is an open set we demonstrate, using quasicrystals, how such $\\Lambda$ can be deterministically constructed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.02619","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}